As
@A1Janitor said, NAPS is not something you can really "get into" in the traditional college sense. The only time I got asked about NAPS during my USNA application was during my Blue and Gold Officer interview and it was simply "Would you accept an appointment to NAPS, if it was offered by USNA?" There is no specific application to NAPS. USNA appoints people to NAPS (and so does USCGA) who are not qualified for an appointment to USNA in some sense (typically academics), but they demonstrate potential to be successful MIDN after a year of training/classes. Be rest assured, if you earned an appointment to USNA, you have the raw potential to succeed there. Admissions has been doing their job for a long time.
Also word to the wise. You being on cross country might come up in an interview at some point. Your interviewer might ask why you joined late. "I just joined for a varsity letter" isn't an ideal response. Something along the lines of "XC allows me to increase my fitness in a structured environment, push myself mentally and physically, and be part of a team in pursuit of a common goal" is more of what people would like to hear. USNA very much views athletics as both physical and leadership development programs. Combat is a team sport in the truest sense of the term